A298732 Number of compositions (ordered partitions) of n into parts > 1 such that no two adjacent parts are equal (Carlitz compositions).

1, 0, 1, 1, 1, 3, 3, 6, 7, 14, 18, 30, 45, 66, 107, 157, 245, 369, 569, 862, 1325, 2020, 3078, 4717, 7183, 10991, 16769, 25626, 39117, 59763, 91264, 139362, 212893, 325060, 496525, 758258, 1158079, 1768634, 2701162, 4125320, 6300303, 9622247, 14695253, 22443451, 34276405, 52348435

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=2} x^k/(1 + x^k)).

Example

a(7) = 6 because we have [7], [5, 2], [4, 3], [3, 4], [2, 5] and [2, 3, 2].

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
      add(`if`(j=i, 0, b(n-j, `if`(j<=n-j, j, 0))), j=2..n))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..50);  # Alois P. Heinz, Jan 25 2018

Mathematica

nmax = 45; CoefficientList[Series[1/(1 - Sum[x^k/(1 + x^k), {k, 2, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000045, A002865, A003242, A011782, A025147, A032020, A114900, A155822, A212804, A218694.

Sequence in context: A056508 A050065 A367394 * A078477 A336077 A360375

Adjacent sequences: A298729 A298730 A298731 * A298733 A298734 A298735

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 25 2018

Status

approved